{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3qNVu3iEXuOV"
      },
      "source": [
        "# Benchmark Statistics\n",
        "#### Tianle Li\\*, Evan Frick\\*\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "snBTNY03dO34"
      },
      "source": [
        "## Install Dependencies"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3kSLAtXFAwwa",
        "outputId": "2704dc57-d9f0-4c4e-c69e-c69ea5fc73a5"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Requirement already satisfied: gdown in /home/tim/miniconda3/lib/python3.10/site-packages (5.1.0)\n",
            "Requirement already satisfied: beautifulsoup4 in /home/tim/miniconda3/lib/python3.10/site-packages (from gdown) (4.12.2)\n",
            "Requirement already satisfied: filelock in /home/tim/miniconda3/lib/python3.10/site-packages (from gdown) (3.12.2)\n",
            "Requirement already satisfied: requests[socks] in /home/tim/miniconda3/lib/python3.10/site-packages (from gdown) (2.31.0)\n",
            "Requirement already satisfied: tqdm in /home/tim/miniconda3/lib/python3.10/site-packages (from gdown) (4.66.1)\n",
            "Requirement already satisfied: soupsieve>1.2 in /home/tim/miniconda3/lib/python3.10/site-packages (from beautifulsoup4->gdown) (2.5)\n",
            "Requirement already satisfied: charset-normalizer<4,>=2 in /home/tim/miniconda3/lib/python3.10/site-packages (from requests[socks]->gdown) (2.0.4)\n",
            "Requirement already satisfied: idna<4,>=2.5 in /home/tim/miniconda3/lib/python3.10/site-packages (from requests[socks]->gdown) (3.4)\n",
            "Requirement already satisfied: urllib3<3,>=1.21.1 in /home/tim/miniconda3/lib/python3.10/site-packages (from requests[socks]->gdown) (2.1.0)\n",
            "Requirement already satisfied: certifi>=2017.4.17 in /home/tim/miniconda3/lib/python3.10/site-packages (from requests[socks]->gdown) (2023.11.17)\n",
            "Requirement already satisfied: PySocks!=1.5.7,>=1.5.6 in /home/tim/miniconda3/lib/python3.10/site-packages (from requests[socks]->gdown) (1.7.1)\n",
            "Retrieving folder contents\n",
            "Processing file 10qErII3BFo9NQ_mrlI5BYdIummYHNFw0 alpaca_2.0_lc_results.jsonl\n",
            "Processing file 1u8ODUn-nw3jLubXeVMVijJQinJVUcwxm alpaca_to_arena.json\n",
            "Processing file 1D8bLtuVMbW2jcc3tooL7q-cS8GWUyLoc arena_to_arena_hard.json\n",
            "Processing file 1FUvSbqtwFk7rdHO9ZVft_6f4Fyd_8d7Y bootstrap_stats_alpaca_LC.jsonl\n",
            "Processing file 1vDTVb-MSkI5rPGl9XanAcO6j15jtlzMO bootstrap_stats_arena_hard.jsonl\n",
            "Processing file 1BAW8RCK9wqNFnrdW7IRhBx6nERAKEZ0C bootstrap_stats_mt_bench.jsonl\n",
            "Processing file 1aPPZOVdPKIZNgBX-yz0wAJj9neh5kbFx elo_results_20240329.pkl\n",
            "Retrieving folder contents completed\n",
            "Building directory structure\n",
            "Building directory structure completed\n",
            "Error:\n",
            "\n",
            "\t[Errno 13] Permission denied: '/content'\n",
            "\n",
            "To report issues, please visit https://github.com/wkentaro/gdown/issues.\n",
            "Collecting scikit-learn==1.3\n",
            "  Downloading scikit_learn-1.3.0-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl.metadata (11 kB)\n",
            "Requirement already satisfied: numpy>=1.17.3 in /home/tim/.local/lib/python3.10/site-packages (from scikit-learn==1.3) (1.25.1)\n",
            "Requirement already satisfied: scipy>=1.5.0 in /home/tim/miniconda3/lib/python3.10/site-packages (from scikit-learn==1.3) (1.11.2)\n",
            "Requirement already satisfied: joblib>=1.1.1 in /home/tim/miniconda3/lib/python3.10/site-packages (from scikit-learn==1.3) (1.3.2)\n",
            "Requirement already satisfied: threadpoolctl>=2.0.0 in /home/tim/miniconda3/lib/python3.10/site-packages (from scikit-learn==1.3) (3.2.0)\n",
            "Downloading scikit_learn-1.3.0-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (10.8 MB)\n",
            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m10.8/10.8 MB\u001b[0m \u001b[31m11.7 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m00:01\u001b[0m00:01\u001b[0m\n",
            "\u001b[?25hInstalling collected packages: scikit-learn\n",
            "  Attempting uninstall: scikit-learn\n",
            "    Found existing installation: scikit-learn 1.4.2\n",
            "    Uninstalling scikit-learn-1.4.2:\n",
            "      Successfully uninstalled scikit-learn-1.4.2\n",
            "Successfully installed scikit-learn-1.3.0\n"
          ]
        }
      ],
      "source": [
        "!pip install --upgrade --no-cache-dir gdown\n",
        "!gdown --folder https://drive.google.com/drive/folders/1dW1SugeP2kh5xM8xSY9bNLZjrkFcZI7N?usp=drive_link -O /content\n",
        "!pip install -U scikit-learn==1.3"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "XXlW90leCEqU"
      },
      "outputs": [],
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "import json\n",
        "\n",
        "from math import comb\n",
        "from tqdm import tqdm\n",
        "from glob import glob\n",
        "from collections import defaultdict\n",
        "\n",
        "import json, math, gdown\n",
        "import plotly.express as px\n",
        "import requests\n",
        "\n",
        "pd.options.display.float_format = '{:.2f}'.format\n",
        "\n",
        "from sklearn.linear_model import LogisticRegression"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yOEhhqHidXft"
      },
      "source": [
        "## Overall Separability\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "D8IHF0Pa5r_6"
      },
      "outputs": [],
      "source": [
        "def get_unique_overlapping_interval_pairs(df, key_lower=\"lower\", key_upper=\"upper\"):\n",
        "    intervals = [[lower, upper] for lower, upper in zip(df[key_lower].tolist(), df[key_upper].tolist())]\n",
        "\n",
        "    # Sort the intervals by start time\n",
        "    intervals.sort(key=lambda x: x[0])\n",
        "\n",
        "    overlapping_pairs = []\n",
        "    for i in range(len(intervals)):\n",
        "        for j in range(i+1, len(intervals)):\n",
        "            # If the start time of the second interval is less than the end time of the first, they overlap\n",
        "            if intervals[j][0] < intervals[i][1]:\n",
        "                # Check if the pair is already in the list\n",
        "                if (intervals[i], intervals[j]) not in overlapping_pairs and (intervals[j], intervals[i]) not in overlapping_pairs:\n",
        "                    overlapping_pairs.append((intervals[i], intervals[j]))\n",
        "            else:\n",
        "                break\n",
        "\n",
        "    return len(overlapping_pairs), comb(len(df), 2)\n",
        "\n",
        "\n",
        "def print_overlap_count(overlap_count, total_count):\n",
        "  print(f\"Overlap Pair #: {overlap_count}, Total model Pair #: {total_count}\")\n",
        "  overlap_percenage = np.round(overlap_count / total_count * 100, decimals=2)\n",
        "  print(f\"Overlapped: {overlap_percenage}%\")\n",
        "  print(f\"Confidence: {100 - overlap_percenage}%\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8y-50pbMC-SV",
        "outputId": "a7d5069f-86de-430a-c66a-67167e3702bd"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Arena Hard:      28 models\n",
            "Overlap Pair #: 76, Total model Pair #: 378\n",
            "Overlapped: 20.11%\n",
            "Confidence: 79.89%\n"
          ]
        }
      ],
      "source": [
        "arena_hard = pd.read_json(\"bootstrap_stats_arena_hard.jsonl\", lines=True) # Arena Hard\n",
        "print(f\"Arena Hard: {len(arena_hard) : >7} models\")\n",
        "overlap_count, total_count = get_unique_overlapping_interval_pairs(arena_hard)\n",
        "print_overlap_count(overlap_count, total_count)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZULsczbDGds5",
        "outputId": "f92a2835-9feb-40ac-dda9-824282dfd41f"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Chatbot Arena:      76 models\n",
            "Overlap Pair #: 258, Total model Pair #: 2850\n",
            "Overlapped: 9.05%\n",
            "Confidence: 90.95%\n"
          ]
        }
      ],
      "source": [
        "elo_results = pd.read_pickle(\"elo_results_20240329.pkl\")\n",
        "elo = elo_results['full']['leaderboard_table_df'].reset_index()\n",
        "print(f\"Chatbot Arena: {len(elo) : >7} models\")\n",
        "overlap_count, total_count = get_unique_overlapping_interval_pairs(elo, \"rating_q025\", \"rating_q975\")\n",
        "print_overlap_count(overlap_count, total_count)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Chatbot Arena (Arena Hard Distribution):      78 models\n",
            "Overlap Pair #: 927, Total model Pair #: 3003\n",
            "Overlapped: 30.87%\n",
            "Confidence: 69.13%\n"
          ]
        }
      ],
      "source": [
        "elo_arena_hard_dist = pd.read_json(\"bootstrap_stats_arena_hard_distribution_elo.jsonl\", lines=True)\n",
        "print(f\"Chatbot Arena (Arena Hard Distribution): {len(elo_arena_hard_dist) : >7} models\")\n",
        "overlap_count, total_count = get_unique_overlapping_interval_pairs(elo_arena_hard_dist)\n",
        "print_overlap_count(overlap_count, total_count)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7qGOMoAajMuA",
        "outputId": "09d1016f-0c40-4fa4-f9ff-5a9611b6bba2"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "MT Bench:      25 models\n",
            "Overlap Pair #: 197, Total model Pair #: 300\n",
            "Overlapped: 65.67%\n",
            "Confidence: 34.33%\n"
          ]
        }
      ],
      "source": [
        "mt_bench = pd.read_json(\"bootstrap_stats_mt_bench.jsonl\", lines=True)\n",
        "print(f\"MT Bench: {len(mt_bench) : >7} models\")\n",
        "overlap_count, total_count = get_unique_overlapping_interval_pairs(mt_bench)\n",
        "print_overlap_count(overlap_count, total_count)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "e0Ke96Gd8qYM",
        "outputId": "78a89ce7-3476-439e-eeb1-4c06d3fc985f"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Alpaca 2.0 LC:      20 models\n",
            "Overlap Pair #: 23, Total model Pair #: 190\n",
            "Overlapped: 12.11%\n",
            "Confidence: 87.89%\n"
          ]
        }
      ],
      "source": [
        "alpaca_lc = pd.read_json(\"bootstrap_stats_alpaca_LC.jsonl\", lines=True)\n",
        "print(f\"Alpaca 2.0 LC: {len(alpaca_lc) : >7} models\")\n",
        "overlap_count, total_count = get_unique_overlapping_interval_pairs(alpaca_lc)\n",
        "print_overlap_count(overlap_count, total_count)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DmozKpknHIYi"
      },
      "source": [
        "## Benchmark Performance on shared 20 models"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Separability with 95% Confidence"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "id": "l_ilgB_2nSP_"
      },
      "outputs": [],
      "source": [
        "alpaca_lc = pd.read_json(\"bootstrap_stats_alpaca_LC.jsonl\", lines=True)\n",
        "alpaca_to_arena = json.load(open(\"alpaca_to_arena.json\"))\n",
        "alpaca_lc[\"model\"] = [alpaca_to_arena[model] for model in alpaca_lc.model]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Alpaca 2.0 LC:      20 models\n",
            "Overlap Pair #: 23, Total model Pair #: 190\n",
            "Overlapped: 12.11%\n",
            "Confidence: 87.89%\n"
          ]
        }
      ],
      "source": [
        "print(f\"Alpaca 2.0 LC: {len(alpaca_lc) : >7} models\")\n",
        "overlap_count, total_count = get_unique_overlapping_interval_pairs(alpaca_lc)\n",
        "print_overlap_count(overlap_count, total_count)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {},
      "outputs": [],
      "source": [
        "alpaca = pd.read_json(\"bootstrap_stats_alpaca.jsonl\", lines=True)\n",
        "alpaca[\"model\"] = [alpaca_to_arena[model] for model in alpaca.model]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Alpaca 2.0:      20 models\n",
            "Overlap Pair #: 55, Total model Pair #: 190\n",
            "Overlapped: 28.95%\n",
            "Confidence: 71.05%\n"
          ]
        }
      ],
      "source": [
        "print(f\"Alpaca 2.0: {len(alpaca) : >7} models\")\n",
        "overlap_count, total_count = get_unique_overlapping_interval_pairs(alpaca)\n",
        "print_overlap_count(overlap_count, total_count)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "id": "S6KHrSMNGgW8"
      },
      "outputs": [],
      "source": [
        "arena_hard = pd.read_json(\"bootstrap_stats_arena_hard.jsonl\", lines=True)\n",
        "arena_to_arena_hard = json.load(open(\"arena_to_arena_hard.json\"))\n",
        "arena_hard_to_arena = {v: k for k, v in arena_to_arena_hard.items()}\n",
        "arena_hard[\"model\"] = arena_hard.model.str.lower()\n",
        "arena_hard = arena_hard[arena_hard.model.isin(list(arena_hard_to_arena.keys()))]\n",
        "arena_hard[\"model\"] = [arena_hard_to_arena[model] for model in arena_hard.model]\n",
        "arena_hard = arena_hard.reset_index(drop=True)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "frFeIinYG8_h",
        "outputId": "69e2332a-fcf3-4ea4-ae3d-614de74edcd0"
      },
      "outputs": [],
      "source": [
        "assert any([a == b for a, b in zip(sorted(list(arena_hard_to_arena.values())), sorted(list(alpaca_to_arena.values())))])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IqCrSjxtHo5T",
        "outputId": "f3480bf7-f34a-4861-9552-931bc110c8e0"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Arena Hard:      20 models\n",
            "Overlap Pair #: 30, Total model Pair #: 190\n",
            "Overlapped: 15.79%\n",
            "Confidence: 84.21000000000001%\n"
          ]
        }
      ],
      "source": [
        "print(f\"Arena Hard: {len(arena_hard) : >7} models\")\n",
        "overlap_count, total_count = get_unique_overlapping_interval_pairs(arena_hard)\n",
        "print_overlap_count(overlap_count, total_count)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {},
      "outputs": [],
      "source": [
        "elo_subset = elo[elo[\"index\"].isin(list(arena_to_arena_hard.keys()))]\n",
        "elo_subset.reset_index(drop=True, inplace=True)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Chatbot Arena:      20 models\n",
            "Overlap Pair #: 16, Total model Pair #: 190\n",
            "Overlapped: 8.42%\n",
            "Confidence: 91.58%\n"
          ]
        }
      ],
      "source": [
        "print(f\"Chatbot Arena: {len(elo_subset) : >7} models\")\n",
        "overlap_count, total_count = get_unique_overlapping_interval_pairs(elo_subset, \"rating_q025\", \"rating_q975\")\n",
        "print_overlap_count(overlap_count, total_count)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 55,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Chatbot Arena (20K votes):      20 models\n",
            "Overlap Pair #: 59, Total model Pair #: 190\n",
            "Overlapped: 31.05%\n",
            "Confidence: 68.95%\n"
          ]
        }
      ],
      "source": [
        "elo_20k = pd.read_json(\"bootstrap_stats_20k_votes.jsonl\", lines=True)\n",
        "print(f\"Chatbot Arena (20K votes): {len(elo_20k) : >7} models\")\n",
        "overlap_count, total_count = get_unique_overlapping_interval_pairs(elo_20k)\n",
        "print_overlap_count(overlap_count, total_count)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {},
      "outputs": [],
      "source": [
        "elo_arena_hard_dist_subset = elo_arena_hard_dist[elo_arena_hard_dist[\"model\"].isin(elo_subset[\"index\"])]\n",
        "elo_arena_hard_dist_subset.reset_index(drop=True, inplace=True)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Chatbot Arena (Arena Hard Distribution):      20 models\n",
            "Overlap Pair #: 45, Total model Pair #: 190\n",
            "Overlapped: 23.68%\n",
            "Confidence: 76.32%\n"
          ]
        }
      ],
      "source": [
        "print(f\"Chatbot Arena (Arena Hard Distribution): {len(elo_arena_hard_dist_subset) : >7} models\")\n",
        "overlap_count, total_count = get_unique_overlapping_interval_pairs(elo_arena_hard_dist_subset)\n",
        "print_overlap_count(overlap_count, total_count)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {},
      "outputs": [],
      "source": [
        "mt_bench = pd.read_json(\"bootstrap_stats_mt_bench.jsonl\", lines=True)\n",
        "arena_to_mt_bench = json.load(open(\"arena_to_mt_bench.json\"))\n",
        "mt_bench_to_arena = {v: k for k, v in arena_to_mt_bench.items()}\n",
        "mt_bench[\"model\"] = mt_bench.model.str.lower()\n",
        "mt_bench = mt_bench[mt_bench.model.isin(list(mt_bench_to_arena.keys()))]\n",
        "mt_bench[\"model\"] = [mt_bench_to_arena[model] for model in mt_bench.model]\n",
        "mt_bench.reset_index(drop=True, inplace=True)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "MT Bench:      20 models\n",
            "Overlap Pair #: 121, Total model Pair #: 190\n",
            "Overlapped: 63.68%\n",
            "Confidence: 36.32%\n"
          ]
        }
      ],
      "source": [
        "print(f\"MT Bench: {len(mt_bench) : >7} models\")\n",
        "overlap_count, total_count = get_unique_overlapping_interval_pairs(mt_bench)\n",
        "print_overlap_count(overlap_count, total_count)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Separability with 80% Confidence"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {},
      "outputs": [],
      "source": [
        "def get_unique_overlapping_interval_pairs_general(df, confidence=[2.5, 97.5]):\n",
        "    intervals = [[np.percentile(interval, confidence[0]), np.percentile(interval, confidence[1])] for interval in df.results]\n",
        "\n",
        "    # Sort the intervals by start time\n",
        "    intervals.sort(key=lambda x: x[0])\n",
        "\n",
        "    overlapping_pairs = []\n",
        "    for i in range(len(intervals)):\n",
        "        for j in range(i+1, len(intervals)):\n",
        "            # If the start time of the second interval is less than the end time of the first, they overlap\n",
        "            if intervals[j][0] < intervals[i][1]:\n",
        "                # Check if the pair is already in the list\n",
        "                if (intervals[i], intervals[j]) not in overlapping_pairs and (intervals[j], intervals[i]) not in overlapping_pairs:\n",
        "                    overlapping_pairs.append((intervals[i], intervals[j]))\n",
        "            else:\n",
        "                break\n",
        "\n",
        "    return len(overlapping_pairs), comb(len(df), 2)\n",
        "\n",
        "\n",
        "def get_unique_overlapping_interval_pairs_elo(df, confidence=[2.5, 97.5]):\n",
        "    intervals = [[np.percentile(df[model], confidence[0]), np.percentile(df[model], confidence[1])] for model in df.columns]\n",
        "\n",
        "    # Sort the intervals by start time\n",
        "    intervals.sort(key=lambda x: x[0])\n",
        "\n",
        "    overlapping_pairs = []\n",
        "    for i in range(len(intervals)):\n",
        "        for j in range(i+1, len(intervals)):\n",
        "            # If the start time of the second interval is less than the end time of the first, they overlap\n",
        "            if intervals[j][0] < intervals[i][1]:\n",
        "                # Check if the pair is already in the list\n",
        "                if (intervals[i], intervals[j]) not in overlapping_pairs and (intervals[j], intervals[i]) not in overlapping_pairs:\n",
        "                    overlapping_pairs.append((intervals[i], intervals[j]))\n",
        "            else:\n",
        "                break\n",
        "\n",
        "    return len(overlapping_pairs), comb(len(df), 2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Alpaca 2.0 LC:      20 models\n",
            "Overlap Pair #: 13, Total model Pair #: 190\n",
            "Overlapped: 6.84%\n",
            "Confidence: 93.16%\n"
          ]
        }
      ],
      "source": [
        "print(f\"Alpaca 2.0 LC: {len(alpaca_lc) : >7} models\")\n",
        "overlap_count, total_count = get_unique_overlapping_interval_pairs_general(alpaca_lc, [10, 90])\n",
        "print_overlap_count(overlap_count, total_count)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Alpaca 2.0:      20 models\n",
            "Overlap Pair #: 33, Total model Pair #: 190\n",
            "Overlapped: 17.37%\n",
            "Confidence: 82.63%\n"
          ]
        }
      ],
      "source": [
        "print(f\"Alpaca 2.0: {len(alpaca) : >7} models\")\n",
        "overlap_count, total_count = get_unique_overlapping_interval_pairs_general(alpaca, [10, 90])\n",
        "print_overlap_count(overlap_count, total_count)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Arena Hard:      20 models\n",
            "Overlap Pair #: 17, Total model Pair #: 190\n",
            "Overlapped: 8.95%\n",
            "Confidence: 91.05%\n"
          ]
        }
      ],
      "source": [
        "print(f\"Arena Hard: {len(arena_hard) : >7} models\")\n",
        "overlap_count, total_count = get_unique_overlapping_interval_pairs_general(arena_hard, [10, 90])\n",
        "print_overlap_count(overlap_count, total_count)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "metadata": {},
      "outputs": [],
      "source": [
        "elo_bootstrap = elo_results[\"full\"][\"bootstrap_df\"]\n",
        "elo_bootstrap_subset = elo_bootstrap[elo_bootstrap.columns[elo_bootstrap.columns.isin(elo_subset[\"index\"])]]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Chatbot Arena:      20 models\n",
            "Overlap Pair #: 13, Total model Pair #: 4950\n",
            "Overlapped: 0.26%\n",
            "Confidence: 99.74%\n"
          ]
        }
      ],
      "source": [
        "print(f\"Chatbot Arena: {len(elo_bootstrap_subset.columns) : >7} models\")\n",
        "overlap_count, total_count = get_unique_overlapping_interval_pairs_elo(elo_bootstrap_subset, [10, 90])\n",
        "print_overlap_count(overlap_count, total_count)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Chatbot Arena (20K votes):      20 models\n",
            "Overlap Pair #: 34, Total model Pair #: 190\n",
            "Overlapped: 17.89%\n",
            "Confidence: 82.11%\n"
          ]
        }
      ],
      "source": [
        "elo_20k = pd.read_json(\"bootstrap_stats_20k_votes_elo.jsonl\", lines=True)\n",
        "print(f\"Chatbot Arena (20K votes): {len(elo_20k) : >7} models\")\n",
        "overlap_count, total_count = get_unique_overlapping_interval_pairs_general(elo_20k, [10, 90])\n",
        "print_overlap_count(overlap_count, total_count)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 31,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Chatbot Arena (Arena Hard Distribution):      20 models\n",
            "Overlap Pair #: 33, Total model Pair #: 190\n",
            "Overlapped: 17.37%\n",
            "Confidence: 82.63%\n"
          ]
        }
      ],
      "source": [
        "print(f\"Chatbot Arena (Arena Hard Distribution): {len(elo_arena_hard_dist_subset) : >7} models\")\n",
        "overlap_count, total_count = get_unique_overlapping_interval_pairs_general(elo_arena_hard_dist_subset, [10, 90])\n",
        "print_overlap_count(overlap_count, total_count)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "MT Bench:      20 models\n",
            "Overlap Pair #: 85, Total model Pair #: 190\n",
            "Overlapped: 44.74%\n",
            "Confidence: 55.26%\n"
          ]
        }
      ],
      "source": [
        "print(f\"MT Bench: {len(mt_bench) : >7} models\")\n",
        "overlap_count, total_count = get_unique_overlapping_interval_pairs_general(mt_bench, [10, 90])\n",
        "print_overlap_count(overlap_count, total_count)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Strict Agreement"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "metadata": {},
      "outputs": [],
      "source": [
        "from itertools import combinations\n",
        "from math import comb"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {},
      "outputs": [],
      "source": [
        "assert any([a == b for a, b in zip(sorted(list(alpaca_lc.model)), sorted(list(elo_subset[\"index\"])))])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Alpaca 2.0 LC (strict): 0.8526315789473684\n"
          ]
        }
      ],
      "source": [
        "count = 0\n",
        "for model_a, model_b in combinations(list(alpaca_lc.model), 2):\n",
        "    score_a = alpaca_lc[alpaca_lc[\"model\"] == model_a].iloc[0][\"score\"]\n",
        "    score_b = alpaca_lc[alpaca_lc[\"model\"] == model_b].iloc[0][\"score\"]\n",
        "    elo_a = elo_subset[elo_subset[\"index\"] == model_a].iloc[0][\"rating\"]\n",
        "    elo_b = elo_subset[elo_subset[\"index\"] == model_b].iloc[0][\"rating\"]\n",
        "\n",
        "    if score_a < score_b and elo_a < elo_b:\n",
        "        count += 1\n",
        "    elif score_a > score_b and elo_a > elo_b:\n",
        "        count += 1\n",
        "print(f\"Alpaca 2.0 LC (strict): {count / comb(len(alpaca_lc), 2)}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 36,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Alpaca 2.0 (strict): 0.8105263157894737\n"
          ]
        }
      ],
      "source": [
        "count = 0\n",
        "for model_a, model_b in combinations(list(alpaca.model), 2):\n",
        "    score_a = alpaca[alpaca[\"model\"] == model_a].iloc[0][\"score\"]\n",
        "    score_b = alpaca[alpaca[\"model\"] == model_b].iloc[0][\"score\"]\n",
        "    elo_a = elo_subset[elo_subset[\"index\"] == model_a].iloc[0][\"rating\"]\n",
        "    elo_b = elo_subset[elo_subset[\"index\"] == model_b].iloc[0][\"rating\"]\n",
        "\n",
        "    if score_a < score_b and elo_a < elo_b:\n",
        "        count += 1\n",
        "    elif score_a > score_b and elo_a > elo_b:\n",
        "        count += 1\n",
        "print(f\"Alpaca 2.0 (strict): {count / comb(len(alpaca), 2)}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 37,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Arena Hard (strict): 0.9157894736842105\n"
          ]
        }
      ],
      "source": [
        "count = 0\n",
        "for model_a, model_b in combinations(list(arena_hard.model), 2):\n",
        "    score_a = arena_hard[arena_hard[\"model\"] == model_a].iloc[0][\"score\"]\n",
        "    score_b = arena_hard[arena_hard[\"model\"] == model_b].iloc[0][\"score\"]\n",
        "    elo_a = elo_subset[elo_subset[\"index\"] == model_a].iloc[0][\"rating\"]\n",
        "    elo_b = elo_subset[elo_subset[\"index\"] == model_b].iloc[0][\"rating\"]\n",
        "\n",
        "    if score_a < score_b and elo_a < elo_b:\n",
        "        count += 1\n",
        "    elif score_a > score_b and elo_a > elo_b:\n",
        "        count += 1\n",
        "print(f\"Arena Hard (strict): {count / comb(len(arena_hard), 2)}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 38,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "MT Bench (strict): 0.868421052631579\n"
          ]
        }
      ],
      "source": [
        "count = 0\n",
        "for model_a, model_b in combinations(list(mt_bench.model), 2):\n",
        "    score_a = mt_bench[mt_bench[\"model\"] == model_a].iloc[0][\"score\"]\n",
        "    score_b = mt_bench[mt_bench[\"model\"] == model_b].iloc[0][\"score\"]\n",
        "    elo_a = elo_subset[elo_subset[\"index\"] == model_a].iloc[0][\"rating\"]\n",
        "    elo_b = elo_subset[elo_subset[\"index\"] == model_b].iloc[0][\"rating\"]\n",
        "\n",
        "    if score_a < score_b and elo_a < elo_b:\n",
        "        count += 1\n",
        "    elif score_a > score_b and elo_a > elo_b:\n",
        "        count += 1\n",
        "print(f\"MT Bench (strict): {count / comb(len(mt_bench), 2)}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 40,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Chatbot Arena (20K votes): 0.9578947368421052\n"
          ]
        }
      ],
      "source": [
        "count = 0\n",
        "for model_a, model_b in combinations(list(elo_20k.model), 2):\n",
        "    score_a = elo_20k[elo_20k[\"model\"] == model_a].iloc[0][\"score\"]\n",
        "    score_b = elo_20k[elo_20k[\"model\"] == model_b].iloc[0][\"score\"]\n",
        "    elo_a = elo_subset[elo_subset[\"index\"] == model_a].iloc[0][\"rating\"]\n",
        "    elo_b = elo_subset[elo_subset[\"index\"] == model_b].iloc[0][\"rating\"]\n",
        "\n",
        "    if score_a < score_b and elo_a < elo_b:\n",
        "        count += 1\n",
        "    elif score_a > score_b and elo_a > elo_b:\n",
        "        count += 1\n",
        "print(f\"Chatbot Arena (20K votes): {count / comb(len(elo_20k), 2)}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Agreement With Confidence"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 41,
      "metadata": {},
      "outputs": [],
      "source": [
        "def get_overlap(a, b):\n",
        "    return max(0, min(a[1], b[1]) - max(a[0], b[0]))\n",
        "\n",
        "def get_interval(df, model):\n",
        "    row = df[df.model == model]\n",
        "    assert len(row) == 1\n",
        "    return (row.iloc[0].lower, row.iloc[0].upper)\n",
        "\n",
        "def get_elo_interval(df, model):\n",
        "    row = df[df[\"index\"] == model]\n",
        "    assert len(row) == 1\n",
        "    return (row.iloc[0].rating_q025, row.iloc[0].rating_q975)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 42,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Alpaca 2.0 LC (With Confidence): 0.8728813559322034\n"
          ]
        }
      ],
      "source": [
        "count = 0\n",
        "total = 0\n",
        "for model_a, model_b in combinations(list(alpaca_lc.model), 2):\n",
        "    score_a = get_interval(alpaca_lc, model_a)\n",
        "    score_b = get_interval(alpaca_lc, model_b)\n",
        "\n",
        "    elo_a = get_elo_interval(elo_subset, model_a)\n",
        "    elo_b = get_elo_interval(elo_subset, model_b)\n",
        "\n",
        "    if get_overlap(elo_a, elo_b) > 0:\n",
        "        continue\n",
        "\n",
        "    total += 1\n",
        "\n",
        "    if get_overlap(score_a, score_b) > 0:\n",
        "        count += 0.5\n",
        "        continue\n",
        "\n",
        "    if score_a < score_b and elo_a < elo_b:\n",
        "        count += 1\n",
        "    elif score_a > score_b and elo_a > elo_b:\n",
        "        count += 1\n",
        "print(f\"Alpaca 2.0 LC (With Confidence): {count / total}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 43,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Alpaca 2.0 (With Confidence): 0.7909604519774012\n"
          ]
        }
      ],
      "source": [
        "count = 0\n",
        "total = 0\n",
        "for model_a, model_b in combinations(list(alpaca.model), 2):\n",
        "    score_a = get_interval(alpaca, model_a)\n",
        "    score_b = get_interval(alpaca, model_b)\n",
        "\n",
        "    elo_a = get_elo_interval(elo_subset, model_a)\n",
        "    elo_b = get_elo_interval(elo_subset, model_b)\n",
        "\n",
        "    if get_overlap(elo_a, elo_b) > 0:\n",
        "        continue\n",
        "\n",
        "    total += 1\n",
        "\n",
        "    if get_overlap(score_a, score_b) > 0:\n",
        "        count += 0.5\n",
        "        continue\n",
        "\n",
        "    if score_a < score_b and elo_a < elo_b:\n",
        "        count += 1\n",
        "    elif score_a > score_b and elo_a > elo_b:\n",
        "        count += 1\n",
        "print(f\"Alpaca 2.0 (With Confidence): {count / total}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 44,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Arena Hard (With Confidence): 0.903954802259887\n"
          ]
        }
      ],
      "source": [
        "count = 0\n",
        "total = 0\n",
        "for model_a, model_b in combinations(list(arena_hard.model), 2):\n",
        "    score_a = get_interval(arena_hard, model_a)\n",
        "    score_b = get_interval(arena_hard, model_b)\n",
        "\n",
        "    elo_a = get_elo_interval(elo_subset, model_a)\n",
        "    elo_b = get_elo_interval(elo_subset, model_b)\n",
        "\n",
        "    if get_overlap(elo_a, elo_b) > 0:\n",
        "        continue\n",
        "\n",
        "    total += 1\n",
        "\n",
        "    if get_overlap(score_a, score_b) > 0:\n",
        "        count += 0.5\n",
        "        continue\n",
        "\n",
        "    if score_a < score_b and elo_a < elo_b:\n",
        "        count += 1\n",
        "    elif score_a > score_b and elo_a > elo_b:\n",
        "        count += 1\n",
        "print(f\"Arena Hard (With Confidence): {count / total}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 45,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "MT Bench (With Confidence): 0.6949152542372882\n"
          ]
        }
      ],
      "source": [
        "count = 0\n",
        "total = 0\n",
        "for model_a, model_b in combinations(list(mt_bench.model), 2):\n",
        "    score_a = get_interval(mt_bench, model_a)\n",
        "    score_b = get_interval(mt_bench, model_b)\n",
        "\n",
        "    elo_a = get_elo_interval(elo_subset, model_a)\n",
        "    elo_b = get_elo_interval(elo_subset, model_b)\n",
        "\n",
        "    if get_overlap(elo_a, elo_b) > 0:\n",
        "        continue\n",
        "\n",
        "    total += 1\n",
        "\n",
        "    if get_overlap(score_a, score_b) > 0:\n",
        "        count += 0.5\n",
        "        continue\n",
        "\n",
        "    if score_a < score_b and elo_a < elo_b:\n",
        "        count += 1\n",
        "    elif score_a > score_b and elo_a > elo_b:\n",
        "        count += 1\n",
        "print(f\"MT Bench (With Confidence): {count / total}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 47,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Chatbot Arena 20K votes (With Confidence): 0.8983050847457628\n"
          ]
        }
      ],
      "source": [
        "count = 0\n",
        "total = 0\n",
        "for model_a, model_b in combinations(list(elo_20k.model), 2):\n",
        "    score_a = get_interval(elo_20k, model_a)\n",
        "    score_b = get_interval(elo_20k, model_b)\n",
        "\n",
        "    elo_a = get_elo_interval(elo_subset, model_a)\n",
        "    elo_b = get_elo_interval(elo_subset, model_b)\n",
        "\n",
        "    if get_overlap(elo_a, elo_b) > 0:\n",
        "        continue\n",
        "\n",
        "    total += 1\n",
        "\n",
        "    if get_overlap(score_a, score_b) > 0:\n",
        "        count += 0.5\n",
        "        continue\n",
        "\n",
        "    if score_a < score_b and elo_a < elo_b:\n",
        "        count += 1\n",
        "    elif score_a > score_b and elo_a > elo_b:\n",
        "        count += 1\n",
        "print(f\"Chatbot Arena 20K votes (With Confidence): {count / total}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "count = 0\n",
        "total = 0\n",
        "for model_a, model_b in combinations(list(arena_hard.model), 2):\n",
        "    score_a = get_interval(arena_hard, model_a)\n",
        "    score_b = get_interval(arena_hard, model_b)\n",
        "\n",
        "    elo_a = get_elo_interval(elo_subset, model_a)\n",
        "    elo_b = get_elo_interval(elo_subset, model_b)\n",
        "\n",
        "    if get_overlap(elo_a, elo_b) > 0:\n",
        "        continue\n",
        "\n",
        "    total += 1\n",
        "\n",
        "    if get_overlap(score_a, score_b) > 0:\n",
        "        count += 0.5\n",
        "        continue\n",
        "\n",
        "    if score_a < score_b and elo_a < elo_b:\n",
        "        count += 1\n",
        "    elif score_a > score_b and elo_a > elo_b:\n",
        "        count += 1\n",
        "print(f\"Arena Hard (With Confidence): {count / total}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Spearman Correlation"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 48,
      "metadata": {},
      "outputs": [],
      "source": [
        "from scipy import stats"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 49,
      "metadata": {},
      "outputs": [],
      "source": [
        "elo_subset = elo_subset.rename(columns={\"index\":\"model\"})"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 50,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Alpaca 2.0 LC: 0.8781954887218045\n"
          ]
        }
      ],
      "source": [
        "merged = pd.merge(elo_subset, alpaca_lc, on=\"model\")\n",
        "res = stats.spearmanr(merged.rating, merged.score)\n",
        "print(f\"Alpaca 2.0 LC: {res.statistic}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 51,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Alpaca 2.0: 0.7578947368421052\n"
          ]
        }
      ],
      "source": [
        "merged = pd.merge(elo_subset, alpaca, on=\"model\")\n",
        "res = stats.spearmanr(merged.rating, merged.score)\n",
        "print(f\"Alpaca 2.0: {res.statistic}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 52,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Arena Hard: 0.932330827067669\n"
          ]
        }
      ],
      "source": [
        "merged = pd.merge(elo_subset, arena_hard, on=\"model\")\n",
        "res = stats.spearmanr(merged.rating, merged.score)\n",
        "print(f\"Arena Hard: {res.statistic}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 53,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "MT Bench: 0.8932330827067668\n"
          ]
        }
      ],
      "source": [
        "merged = pd.merge(elo_subset, mt_bench, on=\"model\")\n",
        "res = stats.spearmanr(merged.rating, merged.score)\n",
        "print(f\"MT Bench: {res.statistic}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 54,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "MT Bench: 0.9819548872180449\n"
          ]
        }
      ],
      "source": [
        "merged = pd.merge(elo_subset, elo_20k, on=\"model\")\n",
        "res = stats.spearmanr(merged.rating, merged.score)\n",
        "print(f\"MT Bench: {res.statistic}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Forecasting"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 36,
      "metadata": {},
      "outputs": [],
      "source": [
        "from scipy.stats import norm\n",
        "from seaborn.objects import Jitter, Plot, Dots\n",
        "from sklearn.metrics import log_loss, brier_score_loss"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 56,
      "metadata": {},
      "outputs": [],
      "source": [
        "def calculate_predictions_and_labels(model_list, pred_ratings, true_stats):\n",
        "    output_records = []\n",
        "    for model_a, model_b in combinations(sorted(model_list), 2):\n",
        "        a_mean = pred_ratings['mean'][model_a]\n",
        "        b_mean = pred_ratings['mean'][model_b]\n",
        "\n",
        "        a_var = pred_ratings['var'][model_a]\n",
        "        b_var = pred_ratings['var'][model_b]\n",
        "\n",
        "        p_a_less_than_b = norm(loc=a_mean - b_mean, scale= np.sqrt(a_var + b_var)).cdf(0)\n",
        "\n",
        "        try:\n",
        "            tru = int(true_stats['rating'][model_a] < true_stats['rating'][model_b])\n",
        "            true_p_a_less_than_b = norm(loc=true_stats['rating'][model_a]  - true_stats['rating'][model_b], scale= np.sqrt(true_stats['variance'][model_a] + true_stats['variance'][model_b])).cdf(0)       \n",
        "        except:\n",
        "            print(f\"Warning: {model_a} or {model_b} not found in list of models in true_stats\")\n",
        "            continue\n",
        "        \n",
        "        output_records.append({\"model_a\": model_a, \"model_b\":  model_b, \"a_mean\": a_mean, \"b_mean\": b_mean, \"p(a<b)\": p_a_less_than_b, \"p_true(a<b)\": true_p_a_less_than_b, \"label\": tru})\n",
        "\n",
        "    return pd.DataFrame.from_records(output_records)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 57,
      "metadata": {},
      "outputs": [],
      "source": [
        "arena_subset = elo[elo[\"index\"].isin(list(arena_to_arena_hard.keys()))]\n",
        "arena_subset = arena_subset.set_index(\"index\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 58,
      "metadata": {},
      "outputs": [],
      "source": [
        "alpaca_lc[\"mean\"] = alpaca_lc.results.map(np.mean)\n",
        "alpaca_lc[\"var\"] = alpaca_lc.results.map(np.var)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 59,
      "metadata": {},
      "outputs": [],
      "source": [
        "arena_hard[\"mean\"] = arena_hard.results.map(np.mean)\n",
        "arena_hard[\"var\"] = arena_hard.results.map(np.var)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 60,
      "metadata": {},
      "outputs": [],
      "source": [
        "alpaca[\"mean\"] = alpaca.results.map(np.mean)\n",
        "alpaca[\"var\"] = alpaca.results.map(np.var)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 61,
      "metadata": {},
      "outputs": [],
      "source": [
        "mt_bench[\"mean\"] = mt_bench.results.map(np.mean)\n",
        "mt_bench[\"var\"] = mt_bench.results.map(np.var)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 62,
      "metadata": {},
      "outputs": [],
      "source": [
        "alpaca_lc_results = calculate_predictions_and_labels(alpaca_lc.model.to_list(), \n",
        "                                                  alpaca_lc.set_index(\"model\")[['mean', 'var']].to_dict(), \n",
        "                                                  arena_subset[[\"rating\", \"variance\"]].to_dict())\n",
        "arena_results = calculate_predictions_and_labels(arena_hard.model.to_list(), \n",
        "                                                 arena_hard.set_index(\"model\")[['mean', 'var']].to_dict(), \n",
        "                                                 arena_subset[[\"rating\", \"variance\"]].to_dict())\n",
        "alpaca_results = calculate_predictions_and_labels(alpaca.model.to_list(), \n",
        "                                                  alpaca.set_index(\"model\")[['mean', 'var']].to_dict(), \n",
        "                                                  arena_subset[[\"rating\", \"variance\"]].to_dict())\n",
        "mt_bench_results = calculate_predictions_and_labels(mt_bench.model.to_list(), \n",
        "                                                  mt_bench.set_index(\"model\")[['mean', 'var']].to_dict(), \n",
        "                                                  arena_subset[[\"rating\", \"variance\"]].to_dict())"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 63,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Alpaca 2.0 LC Log-Loss:  1.9652927160512885\n",
            "Alpaca 2.0 Log-Loss:  1.8408659325008474\n",
            "Arena Hard Log-Loss:  0.3950460397256576\n",
            "MT Bench Log-Loss:  0.3310536497002041\n",
            "\n",
            "Alpaca 2.0 LC Brier-Score-Loss:  0.13472585300420672\n",
            "Alpaca 2.0 Brier-Score-Loss:  0.16421065021224288\n",
            "Arena Hard Brier-Score-Loss:  0.07047865504650436\n",
            "MT Bench Brier-Score-Loss:  0.10082905842501223\n"
          ]
        }
      ],
      "source": [
        "print(\"Alpaca 2.0 LC Log-Loss: \", log_loss(alpaca_lc_results['label'], alpaca_lc_results['p(a<b)']))\n",
        "print(\"Alpaca 2.0 Log-Loss: \", log_loss(alpaca_results['label'], alpaca_results['p(a<b)']))\n",
        "print(\"Arena Hard Log-Loss: \", log_loss(arena_results['label'], arena_results['p(a<b)']))\n",
        "print(\"MT Bench Log-Loss: \", log_loss(mt_bench_results['label'], mt_bench_results['p(a<b)']))\n",
        "print()\n",
        "print(\"Alpaca 2.0 LC Brier-Score-Loss: \", brier_score_loss(alpaca_lc_results['label'], alpaca_lc_results['p(a<b)']))\n",
        "print(\"Alpaca 2.0 Brier-Score-Loss: \", brier_score_loss(alpaca_results['label'], alpaca_results['p(a<b)']))\n",
        "print(\"Arena Hard Brier-Score-Loss: \", brier_score_loss(arena_results['label'], arena_results['p(a<b)']))\n",
        "print(\"MT Bench Brier-Score-Loss: \", brier_score_loss(mt_bench_results['label'], mt_bench_results['p(a<b)']))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 64,
      "metadata": {},
      "outputs": [
        {
          "data": {
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",
            "text/plain": [
              "<seaborn._core.plot.Plot at 0x7ae7d04a9600>"
            ]
          },
          "execution_count": 64,
          "metadata": {
            "image/png": {
              "height": 378.25,
              "width": 509.15
            }
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "Plot(data=alpaca_results, x='p(a<b)', y='p_true(a<b)').add(Dots(), Jitter(x=0.025, y=0.025)).label(title=\"Alpaca 2.0 Predicted Probability vs True Probability\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 65,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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            "text/plain": [
              "<seaborn._core.plot.Plot at 0x7ae7d04a9b70>"
            ]
          },
          "execution_count": 65,
          "metadata": {
            "image/png": {
              "height": 378.25,
              "width": 509.15
            }
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "Plot(data=arena_results, x='p(a<b)', y='p_true(a<b)').add(Dots(), Jitter(x=0.025, y=0.025)).label(title=\"Arena Hard Predicted Probability vs True Probability\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 66,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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            "text/plain": [
              "<seaborn._core.plot.Plot at 0x7ae7cd273760>"
            ]
          },
          "execution_count": 66,
          "metadata": {
            "image/png": {
              "height": 378.25,
              "width": 509.15
            }
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "Plot(data=alpaca_lc_results, x='p(a<b)', y='p_true(a<b)').add(Dots(), Jitter(x=0.025, y=0.025)).label(title=\"Alpaca 2.0 LC Predicted Probability vs True Probability\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 67,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<seaborn._core.plot.Plot at 0x7ae7cd28c400>"
            ]
          },
          "execution_count": 67,
          "metadata": {
            "image/png": {
              "height": 378.25,
              "width": 509.15
            }
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "Plot(data=mt_bench_results, x='p(a<b)', y='p_true(a<b)').add(Dots(), Jitter(x=0.025, y=0.025)).label(title=\"MT Bench Predicted Probability vs True Probability\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 55,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>model_a</th>\n",
              "      <th>model_b</th>\n",
              "      <th>a_mean</th>\n",
              "      <th>b_mean</th>\n",
              "      <th>p(a&lt;b)</th>\n",
              "      <th>p_true(a&lt;b)</th>\n",
              "      <th>label</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>gpt-3.5-turbo-1106</td>\n",
              "      <td>claude-3-sonnet-20240229</td>\n",
              "      <td>18.89</td>\n",
              "      <td>46.78</td>\n",
              "      <td>1.00</td>\n",
              "      <td>1.00</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>gpt-3.5-turbo-1106</td>\n",
              "      <td>llama-2-70b-chat</td>\n",
              "      <td>18.89</td>\n",
              "      <td>11.60</td>\n",
              "      <td>0.00</td>\n",
              "      <td>1.00</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>gpt-3.5-turbo-1106</td>\n",
              "      <td>gpt-3.5-turbo-0613</td>\n",
              "      <td>18.89</td>\n",
              "      <td>24.84</td>\n",
              "      <td>1.00</td>\n",
              "      <td>1.00</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>gpt-3.5-turbo-1106</td>\n",
              "      <td>gemma-2b-it</td>\n",
              "      <td>18.89</td>\n",
              "      <td>3.02</td>\n",
              "      <td>0.00</td>\n",
              "      <td>0.00</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>gpt-3.5-turbo-1106</td>\n",
              "      <td>mixtral-8x7b-instruct-v0.1</td>\n",
              "      <td>18.89</td>\n",
              "      <td>23.28</td>\n",
              "      <td>0.98</td>\n",
              "      <td>1.00</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>185</th>\n",
              "      <td>claude-3-opus-20240229</td>\n",
              "      <td>mistral-large-2402</td>\n",
              "      <td>60.37</td>\n",
              "      <td>37.71</td>\n",
              "      <td>0.00</td>\n",
              "      <td>0.00</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>186</th>\n",
              "      <td>claude-3-opus-20240229</td>\n",
              "      <td>gpt-4-0314</td>\n",
              "      <td>60.37</td>\n",
              "      <td>50.00</td>\n",
              "      <td>0.00</td>\n",
              "      <td>0.00</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>187</th>\n",
              "      <td>claude-2.1</td>\n",
              "      <td>mistral-large-2402</td>\n",
              "      <td>22.72</td>\n",
              "      <td>37.71</td>\n",
              "      <td>1.00</td>\n",
              "      <td>1.00</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>188</th>\n",
              "      <td>claude-2.1</td>\n",
              "      <td>gpt-4-0314</td>\n",
              "      <td>22.72</td>\n",
              "      <td>50.00</td>\n",
              "      <td>1.00</td>\n",
              "      <td>1.00</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>189</th>\n",
              "      <td>mistral-large-2402</td>\n",
              "      <td>gpt-4-0314</td>\n",
              "      <td>37.71</td>\n",
              "      <td>50.00</td>\n",
              "      <td>1.00</td>\n",
              "      <td>1.00</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>190 rows × 7 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "                    model_a                     model_b  a_mean  b_mean  \\\n",
              "0        gpt-3.5-turbo-1106    claude-3-sonnet-20240229   18.89   46.78   \n",
              "1        gpt-3.5-turbo-1106            llama-2-70b-chat   18.89   11.60   \n",
              "2        gpt-3.5-turbo-1106          gpt-3.5-turbo-0613   18.89   24.84   \n",
              "3        gpt-3.5-turbo-1106                 gemma-2b-it   18.89    3.02   \n",
              "4        gpt-3.5-turbo-1106  mixtral-8x7b-instruct-v0.1   18.89   23.28   \n",
              "..                      ...                         ...     ...     ...   \n",
              "185  claude-3-opus-20240229          mistral-large-2402   60.37   37.71   \n",
              "186  claude-3-opus-20240229                  gpt-4-0314   60.37   50.00   \n",
              "187              claude-2.1          mistral-large-2402   22.72   37.71   \n",
              "188              claude-2.1                  gpt-4-0314   22.72   50.00   \n",
              "189      mistral-large-2402                  gpt-4-0314   37.71   50.00   \n",
              "\n",
              "     p(a<b)  p_true(a<b)  label  \n",
              "0      1.00         1.00      1  \n",
              "1      0.00         1.00      1  \n",
              "2      1.00         1.00      1  \n",
              "3      0.00         0.00      0  \n",
              "4      0.98         1.00      1  \n",
              "..      ...          ...    ...  \n",
              "185    0.00         0.00      0  \n",
              "186    0.00         0.00      0  \n",
              "187    1.00         1.00      1  \n",
              "188    1.00         1.00      1  \n",
              "189    1.00         1.00      1  \n",
              "\n",
              "[190 rows x 7 columns]"
            ]
          },
          "execution_count": 55,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "arena_results"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    }
  ],
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